Hi. Welcome to the forum from Louisiana, glad you joined us.
I personally have not tried a cross with McMurray's Big Red Broilers or Rangers in general. I'm not sure if those are comparable to Rangers or not.
I would love to find out what mix the broilers are to do more in depth genetic research, but I'm sure it's a carefully guarded secret.
McMurray is not very forthcoming on what they cross to get those birds. They are obviously not sex links because both the boys and girls are red. In the Q&A they say they are not good for reproduction because they are hybrids, but they don't say why. I know hybrids don't breed true but what part of the recessive genetics would cause a problem? It may be important to what you want to do, it may not.
opinions, and perspectives
If you breed a hybrid you don't get consistent results, whether it is bred to another hybrid or a pure bred chicken. Without knowing what the differences are in their parents you don't know what those inconsistent results might be. It could be something like comb type, eye color, or many other things that wouldn't bother you. But it could be something like final size, growth rate, skin color, egg laying, or something that might be very important to you.
In my opinion if you breed that RIR rooster over the BRB pullet you will get some that you are really happy with and some you are not. The more you hatch the better your chances of getting some good ones. If you breed the best of the ones you'd like to eat and eat the rest, in a few generations you will be hatching mostly chicks you are pretty happy with. That first generation you might get a lot that are not great but that number should go down each generation.
If you are into this for the long haul, this probably isn't a horrible way to start. If you are only interested in the next generation, you are probably not going to be real happy. All this is speculation because we don't know the genetics.